Problem $1$:

Your grandfather would like to share some of his fortune with you. He offers to give you money under one of the following scenarios.

Option $1$: $$13,000($lump sum$)$ now

Option $2$: $$22,000($lump sum$)$ seven years from now

Option $3$: $$2,500$ annual payments for seven years

Calculate the present value of each scenario using a $6\mathrm{.}5\%$ interest rate. Which scenario yields the highest value?

Problem $2$:

Your client is planning their retirement. They would like to retire at age $59$ and have enough money to withdraw $$125,000$ per year for the next $40$ years $($based on family history, they believe they will live to age $99.)$ They plan to invest their savings and expect to earn $6\mathrm{.}0\%$ per year.

How much money must they accumulate by retirement to make their plan work?

If they invested in a high$-$risk venture and were able to earn $14\%$ interest, how much would they need to accumulate at retirement?